AIAA-2002-1337

A JOINED-WING STRUCTURAL WEIGHT MODELING STUDY

Maxwell Blair*

Robert A. Canfield**

* Aerospace Engineer, Air Force Research Laboratory, Air Vehicles Directorate, Wright-Patterson AFB, Ohio, AIAA Associate Fellow ** Associate Professor, Air Force Institute of Technology, Department of Aeronautics and Astronautics, Wright-Patterson AFB, Ohio, AIAA Associate Fellow Abstract An integrated design process for generating high fidelity analytical weight estimations of joined-wing concepts is described. Elements of configuration, structures, aerodynamics and aeroelastic analyses are incorporated. Drag and loads are modeled for sizing fuel and structures to meet range and loiter requirements. The joined-wing is a radical departure from the worlds inventory of vehicles. We are motivated because the joined-wing concept may offer weight savings where structural stiffness is a design constraint. Two crucial non-linear phonomena contribute to structural failure: large deformation aerodynamics and geometric non-linear structures. A correct model of the non-linear aeroelastic model offers the possibility of a successful design that leverages these non-linear effects to the benefit of joined-wing designs. The process reported here is useful because physics-based data is automatically fed into making high level decisions in the unprecedented design of a joined-wing concept. The authors hope this work will contribute toward future development of weight-competitive concepts for commercial and USAF use. The current process required the integration of several software products, including the Adaptive Modeling Language (AML), MSC.ASTROS, MSC.NASTRAN and PanAir. Special functions were added into the AML environment, which automate the structure/aero interface and non-linear trim. Background and Goals The joined-wing concept has been studied by a number of designers and specialists since 1986 when Wolkovich [1] published his concept. Livne has provided a valuable survey paper on these technical developments [2]. Blair et. al. presented their work [3] with the development of a joined-wing design model with variable configuration integrated with automated aerodynamic and structures assessment in a single environment. The current paper is a direct follow-on to this referenced work. Complementing the work presented here is the work of Weisshaar and Lee [4] who have provided significant insight into the important role of flutter in constraining joined-wing design. Another publication of interest is the blended-wing-body design study presented by Wakayama [5]. Here, a common environment has been developed for physics-based modeling of this innovative concept. Another unifying approach toward design is presented in [6]. Here, surface geometry is structured to serve as a unifying medium, with the benefit that this saves on data storage where a number of disciplines interact. The weight advantages of joined-wing design are far from realized. Indeed, some advocates have concluded the joined-wing is not weight competitive with existing commercial carriers. However, these conclusions were based on relatively simple models without the benefit of non-linear aeroelastic modeling. With the development of nonlinear analysis and design tools, researchers at AFRL and AFIT are revisiting the joined-wing concept as a weight-competitive alternative. The goal of the current effort is to combine configuration design with high fidelity FEM-based weight modeling in order to converge on a configuration which simultaneously satisfies the following: Range requirements (fuel scheduling) equilibrium in lift and pitching moment stress in static aeroelastic equilibrium. The particular challenge for a joined-wing design is to overcome the nonlinear buckling response of the aft wing. The current work examines the buckling response of a linear fully stressed design (FSD), but 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Con22-25 April 2002, Denver, ColoradoAIAA 2002-1337This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.M. Blair, R. A. Canfield A Joined-Wing Structural Weight Modeling Study the process is being established to iterate for the nonlinear case. AML for System Design Integration The Adaptive Modeling Language (AML) [7] has been aggressively marketed as an engineering design modeling environment for software developers. As such, it was clear to the authors that AML facilitated the joined-wing design process reported in this paper. AML features which facilitate the process are (a) strongly object-oriented programming language making full use of parent-child relationships and object inheritance (b) native-geometry objects based on Parasolids and Shapes geometry engines (c) interpreted code for run-time interaction and compiled-code for numerical speed (d) automated memory management and (e) automated dependency-tracking and demand-driven calculations. The AML interface drives the analysis modules. PanAir is used as the aerodynamic surface paneling method to calculate steady air loads. ASTROS is used for FSD. MSC.Nastran is used for the buckling and the geometrically nonlinear analysis. Basic AML Objects and Enhancements The design of a joined-wing involves complex geometry beyond what is normally associated with a traditional wing. Here, the first author has taken the tools provided by TechnoSoft and, following standard object inheritance procedures, has tailored a set of objects to serve our needs. The process of developing the joined-wing object has paralleled the development of a set of basic AML objects. Some of the objects, which form the building blocks for the joined-wing object, were reported in [3]. Basic geometric objects were developed to form curves, extruded meshes and Hermite (cubic parametric) surface networks. At the geometric component design level were developed for airfoils, wing panels, extruded wings, wing-tips and joined-wings. These objects are fully controllable. For example, where wing thickness is an important conceptual design feature, a single parameter has been incorporated for its control. In addition, the airfoil object has been enhanced to include tabulated Reynolds-dependent drag polar data. Figure 1. The airfoil object

Figure 2. Wireframe geometry to control wing-panel

Figure 3. The wing object (web geometry)

Figure 4. The wing object (surface geometry)

American Institute of Aeronautics and Astronautics 2M. Blair, R. A. Canfield A Joined-Wing Structural Weight Modeling Study Joined-wing object: A collection of wing-panels, wing-tip, trajectories and contours were used to create a blended surface for the following applications: IGES and ParaSolid surface representations for CFD calculations, panel definitions to drive PanAir input and a structural finite element modeler to drive input for a structural optimization code ASTROS and NASTRAN. This object is controlled with the following properties: scaleable (thickness and chord) airfoils at key locations, twist at key locations, fore-aft wing separation in x and z, component sweep, taper and chord. The shape of the wing tip scales automatically or can be easily crafted to form a variety of shapes such a crescent wing. The web resolution is controlled for each analysis (and IGES model) separately. Aerodynamic Modeling PanAir: PanAir [8] provides the aerodynamic model for large deformations. The element partitioning is variable. The baseline analysis model is depicted in Figure 5. The number of panels is a model variable and is generally between 500 and 1000 depending on convergence. However, little was done to explore aerodynamic convergence with panel refinement. The overall load is calibrated to achieve a fixed lift and therefore, only the distribution of pressure is effected with panel refinement. PanAir is a linear aerodynamic solver using the technique of boundary elements, otherwise referred to as a aerodynamic paneling method. Surface geometry is body-fitted with an array of quadrilateral panels. Continuous surface singularities (both sources and doublets) are distributed using a number of schemes to meet a number of needs. In this work aerodynamic loads were generated from the predicted pressures in the true normal direction. Although the panels form a sharp leading edge and the pressure is assumed normal to the panel, we chose to ignore that information and use the true normal generated by the geometric surface object. The reason for this is to add some element of consistency between the CFD solvers and PanAir. We expect this geometric inconsistency will disappear with PanAir model refinement or its replacement by CFD.

Figure 5. Web Geometry for Joined-wing Concept with 30 degrees tip sweep The aerodynamic mesh incorporates high aspect ratio panels along the inboard portions of the wing and a portion of the outboard wing. The merged region and the wing tip have lower aspect ratio panels to capture spanwise variations in flow. Figure 5 shows that a structured mesh on a joined-wing requires doubling the chord-wise mesh on the outboard leg of the wing. However, this works to our advantage in accurately capturing the outboard portion as we study the loads in the wing joint region. The PanAir model incorporates 12 networks with associated abutments. Each network is a matrix of panels with rows and columns. For instance, the top surface of the aft wing has 8 rows and 7 columns of panels to form a single PanAir network. Flat trailing wakes were placed behind the most aft edge. The wake attached to the trailing edge along the forward and inboard portion of the wing is pre-shaped. No further effort was expended to study the influence of wake shape. Integrated Pressures. PanAir integrates values for rigid-body forces (lift, drag, sideslip) and moments (pitch, roll, yaw). We assume these integrated values are based on constant pressure distributions on each panel and the bordering doublets. PanAir also prints out a file (AGPS) with interpolated pressures at element corner points. For redistributed loads on the structural model, we chose to approximate a smooth pressure distribution based on the pressures at the element corners. However, it turns out there can be a discrepancy of up to 5% between the PanAir integration (based on constant distribution) and our integrated values (based on the interpolated pressure) for a given angle of attack. However, this will not hinder the design of a structure where the total lift is

American Institute of Aeronautics and Astronautics 3M. Blair, R. A. Canfield A Joined-Wing Structural Weight Modeling Study specified and distribution of pressure is subsequently calculated. Trim and Stability Considerations [9]: The center of pressure, defined as x0 = xcp = -MLE/CL, is used to determine the point of static equilibrium. MLE is usually a negative value, so the center of pressure is usually a positive value. Vehicle trim is controlled with angle-of-attack and aft-wing-root-twist . The trim condition is determined with a series of linear Taylor series approximations. [1] )`

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ddCddC ddCddCC C C CM ML LM ML L

CL0 and CM0 are the Taylor reference point in lift and moment coefficient. Two values of (0, 1) and three values of (0, 1, 2) are selected. Panair is very efficient at running multiple angles-of-attack and not efficient with calculations associated with non-linear geometric changes generated by wing-twist. The Taylor reference points (CL0 and CM0) are associated with 1 and 0. The target values of CL and CM are NzW /qS and 0 respectively. Nz is the load-factor. W is the weight. The zero moment is calculated at the center of mass. The system of two equations is solved iteratively for and . Panair is run again for this trim condition and the pressures are again distributed as loads in the structural design. The aerodynamic center is located at xac/c = -CM/CL. The position of the aerodynamic center with respect to the center of mass determines the dynamic pitch stability for the vehicle. Again, dCM/d is usually a negative value so the aerodynamic center is usually a positive value. It turns out that the joined wing concept requires special attention in pitch balance to avoid adverse trim with negative lift on the aft wing resulting in excess drag. This drives the requirement to maintain outboard wing sweep as an important design variable. The zero sweep case is depicted in Figure 6 in order to emphasize this point.

Figure 6. Web Geometry for Joined-wing Concept with 0 degrees tip sweep Drag Build-Up: Aircraft designers decompose drag contributions into three components: (1) parasite drag (2) induced drag (3) compressibility drag. A special utility was developed using incompressible experimental data [10] to account for parasite drag, and ignores compressibility drag. Once high-Reynolds number data is obtained, the procedure will calculate a sectional lift coefficient along each chord-wise column of panels. Values of compressible drag coefficient will then be interpolated from the tabulated two-dimensional drag data. In this way, drag is summed over the wing. While this approach is not reliable for accurate prediction of absolute drag (including fuselage and propeller drag, etc.), it is useful in comparing design variants. Structural Modeling The structural meshes for the upper and lower skins are identical. In addition, the substructure is idealized as a complete egg-crate connecting each top membrane element with its lower counterpart. Soft substructure elements were added at the wingtip leading and trailing edge to facilitate the load transfer between the aerodynamic and structural models. While the incorporation of soft leading and trailing edge structure is non-conventional modeling practice, its inclusion helps us to understand natural load paths for conceptualizing the substructure design. Structural Solution Procedure: The solution procedure for converging on geometric non-linear equilibrium involves use of the standard NASTRAN [11] procedure to solve the global buckling equations. The linear stresses due to flexible, trimmed air loads were used to determine a FSD in ASTROS [12], which was checked for buckling in NASTRAN.

American Institute of Aeronautics and Astronautics 4M. Blair, R. A. Canfield A Joined-Wing Structural Weight Modeling Study Finally, gradient-based optimization in NASTRAN will be used to satisfy the buckling constraint. Aero-Structures Interaction Non-linear analysis requires geometrically large deformations to be addressed. A specialized interface between aerodynamics and structures was generated in AML. The structures-to-aero process finds the intersection between normal vectors at control points in the (undeformed) PanAir model and planar elements in the (undeformed) structural FEM model. The structural deformation between surface grid points is simply interpolated assuming a flat surface. The aero-to-structures process is a bit more involved. Each aerodynamic panel is subdivided and the pressure over each panel is interpolated based on pressure values output at each corner of the PanAir model. The center, normal and integrated-force for each sub-panel is computed and the intersecting structural element is identified. The force is then applied to each element and subsequently to each corner grid point. The force is partitioned according to the proximity to each corner grid, thus maintaining equivalent energy in going from the aerodynamic distribution of pressure to the equivalent structural load at the grid points. The solution procedure for converging on non-linear equilibrium involves a series of corrections starting with a rigid model with rigid loads and ending with flexible loads on a deformed structure. The Joined-Wing Design Process The concept design process is a matter of balancing all design considerations until requirements have been met and the system optimized for cost or performance. A successful design requires a number of conflicting design decisions to be resolved. At the top level, we have to ask if the joined-wing vehicle design has the required range and loiter capability. This question can be answered if we know all the weights and aerodynamic drag for all segments of the mission profile. At the detailed structural level, we have to ask if the vehicle is sufficiently stiff (aeroelasticity) and strong to carry all anticipated loads. These two design activities are mutually dependent. Designing for Fuel: To start the process, we seek the fuel required for a specified mission. We could use sophisticated flight path integration schemes (cf. Ref. 2); however, the Breguet range equation provides important insight in the fundamental design of this joined-wing concept, where V is velocity, C is specific fuel consumption, L/D is the lift to drag ratio and W is weight. The range equation is inverted in order to solve for the fuel requirement for a fixed mission range. [2] ||.|

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iiWWDLCVR1ln Aerodynamic efficiency is realized with high L/D. While lift (L) is a direct consequence of weight (structures, payload, etc), aerodynamics takes primary responsibility for drag (D). Elements that contribute to drag are viscosity and induced losses. These relate primarily to geometric wetted area and aspect ratio respectively. Designing for Trim and Stability: For vertical equilibrium in level flight, lift must equal the weight. For a high altitude concept, this may require significant velocity to generate adequate dynamic pressure to remain aloft in thin air. This may become a limiting factor. At the same time, the long endurance mission requires a significant amount of fuel at takeoff. This has to be considered in modeling the takeoff condition. At the same time, the design has to consider pitch equilibrium. An efficient wing design requires that all lifting surface components contribute positive lift. For the joined-wing depicted in Figure 5, the center of mass must be located sufficiently aft to maintain both pitch equilibrium global positive lift. The concern is that with the center of mass moved too far aft, the system may become unstable in pitch with the center of mass aft of the aerodynamic center. It may be corrected with an active control system (for negative static stability) or the outboard wing component may be designed with less aft sweep. System Analysis Elements: The following outline lists the parallel system analysis elements involved in converging on a design solution. Each element starts with an intelligent assumption to be revisited later. For instance L/D is influenced by vehicle weight and trim. However, one starts with the initial guess. 1. Mission 1.1. Lift/Drag (L/D) 1.1.1. Shape 1.1.1.1. Rigid 1.1.1.2. Flexible 1.1.2. Mach 1.1.3. Reynolds Number 1.2. Component Weights 1.2.1. Empty Weight 1.2.1.1. Structure 1.2.1.2. Non-Structural

New structural design using fully-stressed optimization influences vehicle weight which forces everything to be reconsidered. The stress optimization procedure involves a combination of procedures for calculating minimum weights: Fully stressed optimization Buckling optimization System Design Convergence Procedure: A number of unknowns went into the sizing of the joined-wing concept. The two primary drivers are minimum fuel weight and minimum structural weight. Each of these unknowns is calculated in the following iterative fashion. The constraints in this process are: 1. Required mission (range) 1.1. ingress, loiter, egress 2. Load requirements for structural design 2.1. Pull-up @ 2.5-gs (due to gust) There is no one unique path in converging on an acceptable design. Our accomplishment to date is really in the development of this process by which we can design a joined-wing concept in the presence of mutual dependencies with physics-based models. At this point, we focus on what we have accomplished in developing a viable joined-wing design. The Joined-Wing Design The Design Mission: This study uses the Global Hawk mission profile. Global Hawk data approved for public release (unlimited distribution) 12 August 1999. 1) Takeoff zero ft altitude at 0 NM range 2) Climb to 50K ft altitude for 200 NM 3) Cruise at 50K ft for 3000 NM ingress 4) Loiter at 50-65K ft altitude for 24 hours 5) Cruise at 50K ft altitude for 3000 NM egress 6) Descend to zero ft altitude for 200 NM 7) Land at zero ft altitude Here, we assume an L/D of 24 is achievable at Mach 0.6 for ingress and egress. PanAir will be used to calculate L/D for the flexible wing from full to empty fuel conditions to update the Breguet equation. Between 11 and 20 kilometers altitude, the standard speed of sound is 295 m/s. The velocity on ingress and egress is 178 m/s. Assume velocity at loiter is 118 m/s. Assume coefficient of brake horsepower, Cbhp, is 0.55 and propeller efficiency is assumed to be 0.8.

American Institute of Aeronautics and Astronautics 6M. Blair, R. A. Canfield A Joined-Wing Structural Weight Modeling Study ingress loiter egress Range 3000 nm 5,550 km NA 3000 nm 5,550 km Duration NA 24 hr 8.64E4 sec NA Velocity 0.6 Mach @50K ft 177 m/s 0.4 Mach to 65K ft 118 m/s 0.6 Mach @50K ft 177 m/s C (SFC) 2.02E-4 (1/sec) 1.34E-04 (1/sec) 2.02E-4 (1/sec) Dynamic pressure 2939 Pa 638 Pa 2939 Pa Wa/Wb 1.32 1.62 1.33 Table 1. Baseline Aerodynamic Parameters The Baseline Configuration Configuration: The configuration is driven by a significant number of parameters, some of which are listed in Table 1. A schematic is provided in Figure 6 to help interpret these parameters. For this study, this list of parameters is more extensive than the two authors can address for the initial conceptual design. Hence, these parameters are grouped and prioritized according to importance to aerodynamic and structural efficiency for this study. They are also prioritized as they relate to rigid 6dof stability and configuration in order to point out the extent of work for true design integration. This high-risk design concept will not jeopardize the conclusions reached in this study. Twist actuation could be accomplished by conventional control surfaces. Sib 26.00 m Sob 6.25 m crf 2.50 m cra 2.50 m cm 2.50 m ct 2.50 m xfa 22.00 m zfa 7.00 m

ib 30 deg

ob 30 deg Airfoil FX-60-126-1 Calculated Planform Area 145.0 m2

Calculated Wing Volume 52.2 m3

Table 2. Baseline Configuration Parameters Wing Thickness: Wing thickness is influenced by availability of Conformal Load-bearing Antenna Structures (CLAS) technology. Without CLAS, wing thickness is constrained to contain a large antenna array panel facing the nominal horizon. This results in a thick and less efficient wing. CLAS wraps around the wing and potentially results in a thin wing. Increasing wing thickness enables more fuel to be stored in the wings. From a structures perspective, increased wing thickness results in a more stiff and thus lighter wing. Increased flexibility results in larger deformations and more aeroelastic interaction. The skins have lower aspect ratio elements than the aerodynamic panel model in order to govern the resulting substructure element aspect ratio, which can have a large effect on the wing stiffness. Aft Wing Vertical Offset: A larger vertical offset results in a joined-wing concept with more bending stiffness. The normal vector of the nominal plane contains the joined-wing points in the direction of least stiffness. With no vertical offset, the normal is also vertical and the wing is most flexible in the normal direction. With increasing (aft wing) vertical offset, this normal vector begins to point forward away from the lift vector and toward the drag vector, which is much smaller. Thus, the wing deforms less for the same lift. The load path starts at the wing tip and naturally heads in a direction to achieve a state of least global strain energy. Consider a simple pull-up maneuver with the load vector pointing up. Along the aft wing compression and bending loads are present and pass into the vertical tail and the fuselage. Along the front wing, there are tension and bending loads that pass into the fuselage. The two paths meet and equilibrate in the fuselage.

Figure 6. Planform Configuration

Twist-Actuated Aft Wing: Pitch control is effected with twist actuation of the aft wing. The aft wing pivots about a shaft at the wing root. Actuation is realized with pushrods extending up the vertical tail.

American Institute of Aeronautics and Astronautics 7M. Blair, R. A. Canfield A Joined-Wing Structural Weight Modeling Study The aft wing provides ample control power with minimum drag. Aft-wing stiffness is an important feature in the successful design of this novel control effector concept. Torsional stiffness must be low and bending stiffness must be high. Compliant structural design may help realize this concept. Spanwise slits in the aft wing skin will soften the aft wing in torsion. Reinforcement with soft sub-structure will allow large deformations without excessive torsional control power. Materials: The material for the wing structure is currently isotropic aluminum, although composite materials are anticipated for sensor-craft. Sensor-pointing requirements are expected to make wing structural design to be stiffness driven. To account for fatigue life constraints material allowables were reduced to 103 MPa in normal stress and 55 MPa for shear. A minimum structural thickness of 0.125 cm was imposed. Baseline Empty Weights: The mass model is comprised of structural weight, payload, engine, fuel and other systems. The assumed gross take-off weight and the fuel weights (mass) are recorded in the Table 3. Fuel is carried in the wing and fuselage. Fuel distribution is controlled at the top level. This vehicle model assumes all fuel evenly-distributed through the wing and none in the fuselage for maximum load alleviation. Based on Global Hawk (Wto = 25,600 lb), we assume take-off gross weight for this larger joined-wing concept to be 28,600 kg (63,000 lb). Take the product of all the weight fractions (1.3*1.6*1.3) times the take-off gross weight to obtain the calculated landing weight of 10,050 kg. Thus, the mission consumes 18,600 kg of fuel. Mass (kg) Weight (lbs) Payload 2220 4880 Engine 450 1,000 Fuel 18,580 40,870 Wing Structure 6,070 (guess) 13,350(guess) Fuselage Structure 1200 2640 Tail Structure 100 220 TOTAL 28,620 (assumed) 62,960 (assumed) Table 3. Baseline Weights The engine weight is based on Torenbeeks [13] formula, where [0.35 < WE < 0.55] lb/hp. For target L/D of 24 and lift of 30,800 lbs, drag is 1,280 lb. At a velocity of 584 f/s we get a power requirement of P = (1280 * 584) = 7.48E5 ft-lb/s = 1353 hp. With Torenbeeks formula, this results in an engine weight, WE = (1353 * 0.45) = 609 lbs (not installed). Raymer [14] approximates the installed engine weight is WE-installed = 2.575WE0.922 = 2.575*6090.922 = 951 lbs. This weight is approximated as 1000 lbs in the table. The payload weight of nearly 5,000 lbs accounts for electronic gear. The wing structural weight is guessed at 13,000 lb. The non-structural weights are to be appropriately distributed in the design model at various points in the trajectory (different fuel) and subsequently reflected in the aeroelastic FEM model. The fuselage weight is taken from a formula in [15] for commercial vehicles. We arrive at an estimation of 2640 lb for the fuselage weight. A convergence procedure is proposed here to close on the fuel weight and structural weight to meet load requirements, including fuel and inertial relief, recursively based on structural weight. Structural weight is comprised of wing-skin, wing substructure, tail (parametric) and overall fuselage (parametric model). The sub-structures for this model are fully-populated. This egg-crate substructure does not represent actual production substructure. However, if the minimum gauge is not constrained and allowed to approach small values during fully stressed design process, then one expects the resulting weight will be representative of production substructure (minus fasteners etc). Of course, this does not take local buckling and cutouts into consideration. These details are normally approximated at the conceptual stage and accurately accounted only in the detailed design. Keep in mind that these figures are all based on a number of assumptions that must be explored in the design process outlined here. Indeed, the claim of this paper is that no one really knows how much this joined-wing concept will weigh until a high fidelity study is completed. Fuel Weight: The baseline wing has the volume 52.2 m3 to carry 42,300 kg of fuel (kerosene density of 810 kg/m3). The range analysis, Eq.(2), calls for 18,580 kg of fuel, which occupies 44% of the available volume for fuel in the wing. For structural analysis, fuel stored in the wing provides inertial relief, which counters the aerodynamic load. Therefore, more fuel results in less structural load for this design model. Aerodynamic Trim: In order to generate reasonable static aerodynamic loads, a trim analysis was performed to realize static equilibrium for the rigid airplane using the weights calculated up to this point.

Results The integrated rigid pressure on the top skin (Fig. 7) illustrates the significance of leading edge suction as generated by our PanAir model. This is partially offset by the leading edge drag on the lower. These pressures are independently interpolated for the upper and lower networks. One inconsistency is the pressures on the top network and the bottom network do not agree at the leading edge.

Figure 7. Rigid Trimmed PanAir Pressure Vectors on the Top Skin Figure 8 depicts the forces as they have been transferred from the PanAir pressures to the structural grid points. The force vectors are dependent on the size of the structural elements as depicted in Figure 9. A smaller element accumulates pressure from a smaller area. This accounts for the shift in size of force vectors going from inboard to outboard.

Figure 8. Forces at the structural grid points

Two design models initially were used to arrive at a fully stressed design for the flexible, trimmed loads based on linear finite element analysis. The first model sized element thicknesses according to 16 design variables. The second model independently sized 869 element thicknesses. In the first case, the wing was divided into four partitions: forward wing inboard of the joint, aft wing, joint area, and outboard wing. Within each partition elements were grouped as top skin, bottom skin, spars, and ribs, leading to 16 design variable groups. In both cases, only elements within the confines of the structural wing box (front to rear spars and root to tip ribs) were designed. The design variable linking in the first model turned out to be too coarse. The FSD designed structural mass was ten times greater than the FSD designed structural mass for the second case. Comparison of Figures 9 and 10 demonstrates that the nonlinear response of the aft wing is critical. A linear buckling analysis for the first case indicated that the critical load for stability was exceeded by a factor of three. In a fully geometrically nonlinear analysis, the stress exceeded the linear stress by a factor of 16. These results show the importance of including the geometrically nonlinear response in the design.

Figure 10. Fully Stressed DesignNon-Linear Analysis Conclusion While significant progress has been made, this joined-wing design procedure is not yet complete for developing weight estimations based on non-linear aeroelastic design models. Drag estimation requires a complete model including all effects. Here, induced drag was calculated for wing drag build-up, but a parametric model for parasitic drag was not used. Only a constant parasite drag coefficient of 0.01 was assumed. After buckling studies using converged PanAir loads, we will turn our attention on converging the combined non-linear aero and structural model to equilibrium condition. This result will be compared with the buckling study to validate the results. One interesting question needs to be addressed. We have noted that the buckling mode shape tends to unload the outboard wing tip (for washout). We are curious if this effect can be leveraged to produce an aeroelastically fail-safe joined-wing design. Other aeroelastic issues to be addressed are handling qualities, especially for takeoff and landing in the presence of gusts. One of the problems that we face is how to optimize a component at the system level. This works if the interactions are relatively minor, such as a conventional structural optimization to minimize weight. For the joined-wing, we need to consider that the antenna may be carrying loads and it certainly will be consuming power and generating heat. Advanced technology suggests that this joined-wing/antenna structure could also be fully adaptive, i.e. actuated to accomplish other functions such as vehicle control and drag reduction. This advanced structure will be completely integrated with the vehicle and the other subsystems, and will need a different approach for credible analysis and optimization.